Within recent years, allotropic structures of carbon have been produced in the forms of tubes and ribbons which offer the promise of extraordinary electronic and thermal properties. Here we present analyses of oligophenyl and oligoacene systems–infinite, one-dimensional chains of benzene rings linked along the armchair and zigzag directions. These one-dimensional structures, which are amenable to calculation by analytical means, exhibit features very similar to carbon nanotubes and nanoribbons. Using a tight-binding Hamiltonian we analytically determine the density of states, local density of states, and energy-band structure for the phenyl and the acene. We also examine the effect of disorder on the energies and the corresponding states.